Advanced Methods of Structural Analysis

554 Appendix

Ta b l e A. 3 (continued)

No Loading conditions

Reactions and bending

moment diagrams

Expressions for bending

moments and reactions

4

(u+u=1)

M

ul ul

C RA RB

MA

MA

ul ul

MCA

MCB

MA

MCA

MCB

u^2 < 1/3

u^2 < 1/3

MA

u = 0 M

MADM 2  1 3^2 

MCBD3M 2  1 ^2



RADRBD3M2l 1 ^2 

uDD0:5WMADM 8

RADRAD^98 Ml

MCAD 167 MIMCBD 169 M

D 0 WMADM=2

RADRBD3M2l

5

q R

A

RB

MA

MA

MADql

2

8 ;M

l

2



Dql

2

16

RAD^58 qlIRBD^38 ql

6
q RA

RB

MA

MA

MADql

2

15 ;

RAD^25 ql; RBD 101 ql

7

q RA

RB

MA

MA

MAD7ql

2

120 ;

RAD 409 ql; RBD^1140 ql

8

Temperature gradient

t 1

t 2

RA RB

MA

MA

MAD^3 EI ̨.2ht^1 t^2 /

RADRBD^3 EI ̨.2hlt^1 t^2 /

(^9) q
ul
RA
RB
MA
MA
MADql
2
8 u
(^2) .2u/ (^2) Dql (^2) k 1 ;
RBDqa 2 uqlk 1 ;RADqaRB
u k 1 u k 1
0:2 0:0162 0:6 0:0882
0:4 0:0512 0:8 0:1152
0:5 0:0703 1:0 0 : 1250